Gravit. rotational energy related to KE

[katewhitney]

"Consider a system of just two particles, with identical masses, orbiting in circles about their center of mass. SHow that the gravitational potential energy of this system is -2 times the total kinetic energy.

Homework Equations

KE = 1/2 mv^2
U(potential) = -2U(kinetic)
grav. potential =
U=-GMm-r

The Attempt at a Solution

we're supposed to set 1/2mv^2 to the rotational gravitational energy -- but I think i have the wrong equation and I don't know where to go from here...

 

[tiny-tim]

Welcome to PF!

"Consider a system of just two particles, with identical masses, orbiting in circles about their center of mass. SHow that the gravitational potential energy of this system is -2 times the total kinetic energy.

Hi kate! Welcome to PF!

Hint: find the force on each particle, and balance it with the centripetal acceleration to find v.